# Divisible sandpile on Sierpinski gasket graphs

## TL;DR

This paper studies the divisible sandpile model on Sierpinski gasket graphs, showing the shape is a graph metric ball and providing an exact odometer function, advancing understanding of growth models on fractal structures.

## Contribution

It demonstrates the shape of the divisible sandpile on SG is a graph metric ball and derives an exact odometer function, extending growth model analysis to fractal graphs.

## Key findings

- Shape of sandpile is a graph metric ball on SG
- Exact odometer function derived for SG sandpile
- Advances understanding of growth models on fractals

## Abstract

The divisible sandpile model is a growth model on graphs that was introduced by Levine and Peres as a tool to study internal diffusion limited aggregation. In this work we investigate the shape of the divisible sandpile model on the graphical Sierpinski gasket SG. We show that the shape is a ball in the graph metric of SG. Moreover we give an exact representation of the odometer function of the divisible sandpile.